Collisional study of Hilda and quasi-Hilda asteroids

Context. The Hilda asteroids are located in the outer main belt (MB) in a stable 3:2 mean-motion resonance (MMR) with Jupiter, while the quasi-Hildas have similar orbits but are not directly under the effect of the MMR. Moreover, cometary activity has been detected in quasi-Hildas. Aims. In this study, we aim to investigate the collisional evolution of Hilda asteroids and apply it to an investigation into the cratering on asteroid (334) Chicago; we also intend to determine whether impacts between Hildas and quasi-Hildas can serve as a viable mechanism for inducing cometary activity. Methods. Using the Asteroid Collisions and Dynamic Computation (ACDC) code, we simulated the collisional evolution of Hilda asteroids over a period of 4 Gyr. We considered three initial size-frequency distributions (SFDs) and two scaling laws for the collisional outcomes and performed a large set of simulations for each scenario, which we used to construct median SFDs of the Hilda population. We also derived an impactor SFD on asteroid (334) Chicago and used it to calculate the crater SFD on (334) Chicago. Additionally, we evaluated the sub-catastrophic impact timescale between Hilda and quasi-Hilda objects. Results. The observed SFD of Hilda asteroids larger than 3 km is best matched by scenarios assuming that such an SFD is mostly primordial, implying minimal collisional activity over time. For smaller sizes, although unconstrained, the SFD steepens significantly due to the catastrophic fragmentation of a small number of multi-kilometre-sized bodies. We determined that the largest impactor on (334) Chicago measures a few kilometres in size, resulting in a maximum crater size of approximately 30 km. Furthermore, the slope of the crater SFD mirrors that of the initial SFD for sub-kilometric bodies. While impact events between Hildas and quasi-Hildas can induce observable activity, and although it is stochastic in nature, the timescale of such events exceeds the dynamical lifetime of quasi-Hildas, making them an unlikely primary mechanism for inducing observable activity.